In an ac circuit an alternating voltage $200 \sqrt{2} \sin 100 t$ volts is connected to a capacitor

Question

In an ac circuit an alternating voltage $200 \sqrt{2} \sin 100 t$ volts is connected to a capacitor of capacity $1 \mu \mathrm{~F}$. The r.m.s. value of the current in the circuit is\

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(d) : The given equation of alternating voltage is $$ e=200 \sqrt{2} \sin 100 t 	ag{i} $$ The standard equation of alternating voltage is $$ e=e_{0} \sin \omega t 	ag{ii} $$ Comparing (i) and (ii), we get $$ e_{0}=200 \sqrt{2} \mathrm{~V}, \omega=100 \mathrm{rad} \mathrm{~s}^{-1} $$ The capacitive reactance is $$ X_{C}=\frac{1}{\omega C}=\frac{1}{100 	imes 1 	imes 10^{-6}} \Omega $$ The r.m.s. value of the current in the circuit is\ $i_{	ext {r.m.s. }}=\frac{v_{	ext {r.m.s. }}}{X_{C}}=\frac{e_{0} / \sqrt{2}}{1 / \omega C}=\frac{(200 \sqrt{2} / \sqrt{2})}{\left(1 / 100 	imes 10^{-6}ight)}$\ $=200 	imes 100 	imes 10^{-6} \mathrm{~A}=2 	imes 10^{-2} \mathrm{~A}=20 \mathrm{~mA}$\